Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”?
Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied ...
I am asking for a list of concepts which some sources present as definitions whereas other sources pose them as propositions/theorems. For example, most abstract algebra books will define a group ...